Motion In One Dimension Test

Result

Motion In One Dimension Test - 3

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0

A particle has an initial velocity of 9 m/s due east and a constant acceleration of 2 m/s² due west. The distance covered by the particle in the fifth second of its motion is

A
0 m

B
0.5 m

C
2 m

D
None of these

Solution

The displacement is indeed 0 but not the distance. The distance covered is 0.5 m.

Actually, the car is changing the direction of motion at 4.5 seconds. As such, displacement between 4 and 5 seconds is 0 but still the car covers some distance.

The distance is the mod of displacement made by the car between 4 and 4.5 seconds + mod of the displacement between 4.5 and 5 seconds.

Displacement b/w 4 to 4.5 seconds = (9)(0.5) - (4.5²- 4²) = 4.5 - 4.25 = 0.25

Displacement b/w 4.5 to 4 seconds = (9)(0.5) - (5²- 4.5²) = 4.5 - 4.75 = -0.25

Displacement = 0, Distance = 0.5 m
Question 2
1 / -0

A particle experiences constant acceleration for 20 s after starting from rest. If it travels a distance s₁ in the first 10 seconds and distance s₂ in the next 10 seconds, then

A
s₁ = s₂

B
s₂ = 3s₁

C
s₂ = 4s₁

D
s₂ = 5s₁

Solution

s = ut + 1/2at²

u = 0 m/sec (body starts from rest)

s₁= 1/2at²

s₁= 1/2a(10² )

s₁= 50a ------------------(1)

In the next 10 seconds, distance travelled is s₂.

Forthefirst 20 seconds, distance travelled will be s₁ + s₂.

s₁+ s₂= 1/2a(20)²

s₁ + s₂= 200a

Therefore, s₂ = 150a -----------(2)

Now, from equation 1 and 2, we have

s₁/s₂= 50a/150a

s₂= 3s₁